Nuno Espirito Santo's side were about to grab a crucial win in their European quest, thanks to a sublime volley from 26-goal star striker Raul Jimenez.
But referee Mike Dean and VAR stole the spotlight as Matt Doherty, while Chris Wood tried an overhead kick, was harshly deemed to have handled the ball.
Wood scored from the spot deep into added-on time, with Wolves - after losing right at the end at Sheffield United last week, too - left cursing their luck.
This was a brutal reminder of how one incident can drastically change the mood and outlook.
After Jimenez's wonderful volley, the mood was ever-so rosy. Three points would have gone a long way to sealing a Europa League berth.
But now, the Champions League hopes are all but mathematically over and the heat is truly on when it comes to the Europa.
The match with Crystal Palace is suddenly a must-win - after a questionable call by Dean, which was backed up by VAR.
Doherty, you could very much argue, was looking to protect himself from Wood's high boot.
But instead of getting a free-kick for dangerous play, Wolves were handed the bitterest pill to swallow. So tough to take.
Wolves remain sixth, but there is very little room for error in the final two games while they will be hoping some other results go their way.
Nuno, once again, turned heads with his team selection. He made four changes to the side which beat Everton 3-0, most notably opting to play Adama Traore and Ruben Vinagre as the wing-backs.
Joao Moutinho returned to central midfield, and Diogo Jota - who ended his drought against the Toffees - came in on the left of the front three.
It was a massively bold move, looking to get at the Clarets - who predictably lined up in a 4-4-2 with the usual, dependable personnel - right from the off.
With Pedro Neto - fit enough to be involved despite struggling with cramp last weekend - the only major attacking threat on the bench, though, it was also a pretty risky decision from Nuno.
It was particularly intriguing to see how Vinagre would fare against Sean Dyche's physical charges, given his lack of minutes since the restart, while Traore - on his last start at Sheffield United - dislocated his shoulder for the fourth time this campaign.
The speedy duo had the potential to play a huge part in proceedings, and the attacking intent was instantly displayed as Traore won a corner after a minute - and carried on looking to run at Charlie Taylor.
He sent over a trademark cross to Jimenez, who could not quite get enough on the header, which sailed straight at Nick Pope.
Positive, ambitious play from Vinagre - getting around veteran Phil Bardsley - then resulted in another corner, from which Wolves should have taken the lead. Moutinho's inswinger ended up being sent over from close range by Romain Saiss - head in hands.
It was a very positive start from Nuno's side, though, with Burnley struggling to get out of their own half.
Traore looked threatening every time against Taylor, who went on to pull up injured on the half-hour mark, while Moutinho's deliveries were back to a high standard.
As the half approached its close, though, the tempo dropped slightly. Daniel Podence - retaining his place after his superb first start against Everton - was guilty of trying to do too much as his wasteful back-heel ended a promising attack.
But Wolves would still create a massive opportunity before the interval. A much better piece of work from Podence set up Jota, who took a touch before firing into the side netting when he should have at least tested Pope.
You wondered if Nuno's men would come to rue their first-half misses.
The Clarets - who had only managed a Jay Rodriguez shot, which was brilliantly blocked by Conor Coady - began the second period on the back foot, too.
Patient build-up play from Wolves saw Moutinho float the ball to Traore, who worked himself a yard of space on the right of the box and smashed it narrowly past the far post. Jimenez then put one over from a similar position after being found by Podence.
Aiming to find a way into the encounter, Dyche made a switch as former Albion man Rodriguez went off for another ex-Baggie, Matej Vydra.
And they did fashion an opportunity as Josh Brownhill had a go, only for the busy Ruben Neves to, crucially, get in the way.
Burnley, while not peppering the Wolves defence, were growing in confidence.
The visitors replied with long-range shots from both Neves and Podence - straight at Pope and not far wide of the mark, respectively.
Wolves made a change of their own in the 69th minute as Doherty replaced Podence, with Traore joining the forwards.
And shortly after came Jimenez's moment of magic - a stupendous strike
Doherty's effort was blocked, but Jimenez, the magnificent Mexican, found the far corner with a thunderous volley.
That would have been a wonderful way to win it, but Wood - although he missed a glaring header - had other ideas.
The home side were awarded a spot-kick as Doherty - after VAR had a long look at it - was deemed to have handled the ball in the box, and target man Wood emphatically tucked it away. A sickening blow for Wolves.
Burnley (4-4-2): Pope; Bardsley, Tarkowski (c), Long, Taylor (Gudmundsson, 29); Pieters, Brownhill (Brady, 85), Westwood, McNeil; Rodriguez (Vydra, 50), Wood
Goal: Wood (90+6)
Subs not used: Peacock-Farrell (gk), Thompson, Dunne, Benson, Goodridge, Driscoll-Glennon
Wolves (3-4-3): Patricio; Boly, Coady (c), Saiss; Traore, Moutinho, Neves, Vinagre (Otto, 84); Podence (Doherty, 69), Jimenez (Dendoncker, 84), Jota (Neto, 78)
Subs not used: Ruddy (gk), Kilman, Buur, Jordao, Gibbs-White
Goal: Jimenez (76)
Referee: Mike Dean (Wirral)